[R-sig-ME] Another case of -1.0 correlation of random effects

[Kevin E. Thorpe]

Andrew Dolman wrote:
> Shouldn't your preferred model be coded:
> 
> (lmer1 <- lmer(iAUC~Treatment+Dose+(Treatment+Dose|Subject),data=gluc))
> 
> 
> Linear mixed model fit by REML
> Formula: iAUC ~ Treatment + Dose + (Treatment + Dose | Subject)
>    Data: gluc
>   AIC  BIC logLik deviance REMLdev
>  1107 1132 -543.3     1106    1087
> Random effects:
>  Groups   Name         Variance Std.Dev. Corr         
>  Subject  (Intercept)  8402.295 91.6640               
>           TreatmentOat 1736.103 41.6666  -0.097       
>           Dose           30.774  5.5474  -0.883 -0.335
>  Residual              4100.082 64.0319               
> Number of obs: 96, groups: Subject, 12
> 
> Fixed effects:
>              Estimate Std. Error t value
> (Intercept)   313.198     29.076  10.772
> TreatmentOat   -6.673     17.763  -0.376
> Dose          -13.617      2.729  -4.990
> 
> Correlation of Fixed Effects:
>             (Intr) TrtmnO
> TreatmentOt -0.225      
> Dose        -0.687 -0.133
> 
> 
> Which kind of works but you still have a very high correlation between 2 
> random effects.
> 
> 
> Your problems stem, i think, from the fact that there's a very high 
> correlation between the slope of Dose and the Intercept, i.e. subjects 
> with initially higher iAUC respond more strongly to increasing doses of 
> the treatment. You can help the estimation by re-coding Dose so that the 
> intercept is estimated for the highest dose rather than the smallest.
> 
> 
> (lmer1 <- 
> lmer(iAUC~Treatment+I(Dose-8)+(Treatment+I(Dose-8)|Subject),data=gluc))
> 
> Linear mixed model fit by REML
> Formula: iAUC ~ Treatment + I(Dose - 8) + (Treatment + I(Dose - 8) | 
> Subject)
>    Data: gluc
>   AIC  BIC logLik deviance REMLdev
>  1107 1132 -543.3     1106    1087
> Random effects:
>  Groups   Name         Variance Std.Dev. Corr         
>  Subject  (Intercept)  3189.270 56.4736               
>           TreatmentOat 1736.099 41.6665  -0.421       
>           I(Dose - 8)    30.773  5.5474  -0.647 -0.335
>  Residual              4100.085 64.0319               
> Number of obs: 96, groups: Subject, 12
> 
> Fixed effects:
>              Estimate Std. Error t value
> (Intercept)   204.264     21.214   9.629
> TreatmentOat   -6.673     17.763  -0.376
> I(Dose - 8)   -13.617      2.729  -4.990
> 
> Correlation of Fixed Effects:
>             (Intr) TrtmnO
> TreatmentOt -0.446      
> I(Dose - 8)  0.088 -0.133
>  
> 
> Andy.

Thank you very much Andy.  This is extremely helpful.

Thanks also to everyone else who looked at my problem and made 
suggestions.  Mixed-effects models are relatively new to me and I still 
feel not quite at home with them.

Kevin

-- 
Kevin E. Thorpe
Biostatistician/Trialist, Knowledge Translation Program
Assistant Professor, Dalla Lana School of Public Health
University of Toronto
email: kevin.thorpe at utoronto.ca  Tel: 416.864.5776  Fax: 416.864.3016